Question

The order of the following differential equation is \(\underline{\hspace{2cm}}\). [in integer] \[ \left(\frac{dy}{dx}\right)^{2} + 5\frac{dy}{dx} + 4y = 5x^{3} \]

Hint:

The order of a differential equation is determined by the highest derivative present, regardless of powers or nonlinear terms.

Answer 1

Correct Answer: 1

The highest derivative present in the differential equation is \[ \frac{dy}{dx} \] Even though it appears as \((dy/dx)^2\), the order of a differential equation depends only on the highest order derivative, not on its power. Since the only derivative present is the first derivative, the order is: \[ \boxed{1} \]